Question: Simplify the following expression: $ r = \dfrac{-7}{4} + \dfrac{y - 3}{y + 3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y + 3}{y + 3}$ $ \dfrac{-7}{4} \times \dfrac{y + 3}{y + 3} = \dfrac{-7y - 21}{4y + 12} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{y - 3}{y + 3} \times \dfrac{4}{4} = \dfrac{4y - 12}{4y + 12} $ Therefore $ r = \dfrac{-7y - 21}{4y + 12} + \dfrac{4y - 12}{4y + 12} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-7y - 21 + 4y - 12}{4y + 12} $ $r = \dfrac{-3y - 33}{4y + 12}$